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We propose and study a class-expansion/innovation/loss model of genomeevolution taking into account biological roles of genes and their constituentdomains. In our model numbers of genes in different functional categories arecoupled to each other. For example, an increase in the number of metabolicenzymes in a genome is usually accompanied by addition of new transcriptionfactors regulating these enzymes. Such coupling can be thought of as aproportional "recipe" for genome composition of the type "a spoonful of sugarfor each egg yolk". The model jointly reproduces two known empirical laws: thedistribution of family sizes and the nonlinear scaling of the number of genesin certain functional categories (e.g. transcription factors) with genome size.In addition, it allows us to derive a novel relation between the exponentscharacterising these two scaling laws, establishing a direct quantitativeconnection between evolutionary and functional categories. It predicts thatfunctional categories that grow faster-than-linearly with genome size to becharacterised by flatter-than-average family size distributions. This relationis confirmed by our bioinformatics analysis of prokaryotic genomes. This provesthat the joint quantitative trends of functional and evolutionary classes canbe understood in terms of evolutionary growth with proportional recipes.

Joint scaling laws in functional and evolutionary categories in prokaryotic genomes